Problem: Rewrite as a simplified fraction. ${2.\overline{54} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 254.5454...\\ 1x &= 2.5454...\end{align*}}$ Subtracting the two equations, we have: ${99x = 252}$ ${x = \dfrac{252}{99}} $ ${x = \dfrac{28}{11}} \text{or} {2 \dfrac{6}{11}}$